2. Consider the triangle with vertices at A = (0,0), B = (-6, –9), and C = (-15,0). (a) Find the centroid. What special lines did you use to find the centroid? (b) Find the circumcenter. What special lines did you use to find the circumcenter? (c) Find the distance between the circumcenter and the centroid.

Q: Determine the acute angle, in degree measurement, between the planes 2x+2y-1z = -3 and 5x+3y + 2z =…

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Q: considerer the following three points A=(-1,-1), B=(1,3) and c=(3,7) a) find the three distances AB,…

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Q: A) Find the area of the triangle with vertices A (1, -1, -1), B (1, 1, -2) and C (0, -2, -3). B)…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: B- Vertices of a triangle are, A(-1, 0, 1), B(3, -2, 0) and C(4, 1, -2). Find 1- Area of Triangle 2-…

A: A detailed solution is given below.

Q: What are the vertices of the image r(90°, O) (△BCD)?   A. B'(−3, −3), C'(−1, 4), D'(2, 0)   B.…

A: First let us divide the graph into four quadrants Quadrant I   - Both x-axis and y-axis values are…

Q: Consider points A(4, -1, 3), B(3, 1, 8), and C(1, -3, -3). (a) Find the area of parallelogram ABCD…

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Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

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Q: (2, 3.5)

A: Here, the given function is,

Q: Given the triangle J, with vertices J=(0,0), K=(3,1), and L=(-2,6). FIND the coordinates of its…

A:

Q: Find the coordinates of the midpoint of the segment that joins the points a) (a, 0) and (0, b). b)…

A: Givena a, 0 and 0, bb 2a, 0 and 0, 2bMidpoint =x1 +x22 , y1+y22

Q: 1. Consider triangle AABC on the coordinate plane. Let P = (-2, 1) and Q = (2,1). Point P is on side…

A: We are authorized to solve only 3 subpart of question, please repost remaining parts

Q: The vertices of a triangle are (2, 3), (-4, 6), and (2, -6) 1. Determine the ordinate of the…

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Q: A rectangle ha verices at P (6, 6), Q (6, -6), R (-6, -6) and S (-6, 6). The origin is the center of…

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Q: 9. Plot these three coordinate points on the given Cartesian Plane: (2,3) (-2,1) (4,-1) Join the…

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Q: 5. The grid at the right has the segment AB drawn with endpoints at 4(-7,3) and B(5,8). (a) Draw the…

A: After reflection x coordinate replaced with y coordinate and y coordinate with x coordinate

Q: 2. Let ~v = h3,-2,1i and w = h-1,4,2i. (a) Find cos(0) where 0 is the angle betwen ~v and w.

A: Given,   v→=3,-2,1 and w→=-1,4,2

Q: Suppose a triangle has the following vertices: v1 = (5, 0, 2) v2 = (-2, 3, 6) v3 = (3, -3, 1) I…

A: As per the question we are given the 3d coordinates of a triangle as : v1 = (5, 0, 2) v2 = (-2, 3,…

Q: (a) Find the area of the parallelogram with edges v(3,2) and w= = (1, 4).

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Q: Use this formula to find the distance from the point P= (-2,3) to the line 3r – 4y + 5 = 0. 2. Let P…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.